Abstract— We propose two policies to select the route for an adaptive-alternative routing algorithm for all-optical networks. We use the NrPSR to find the Nr routes with lower cost for a given source-destination pair according to a cost function expanded in a power series (PSR) in which the coefficients are determined by a Particle Swarm Optimizer (PSO). The selected route to attend to the call request can be chosen among the Nr found routes depending on the adopted policy. In the first proposal, named NrPSR(OSNRJE), we select the route that presents the lower OSNR that attends the Quality of Transmission requirements. In the second approach, named NrPSR(OSNRMAX), we select the route that presents the higher OSNR. In our simulations we considered some physical layer effects, such as: ASE noise generation, Optical Amplifier gain and ASE saturation and OXC crosstalk. We compared the performance of our proposed policies to others previous proposed policies for the NrPSR and other well known algorithms described in the literature. NrPSR(OSNRJE) outperformed all other routing algorithms.
Index Terms— Optical Networking, Routing and Wavelength Assignment, Wavelength Division Multiplexing, Particle Swarm Optimization.
I. INTRODUCTION
Optical Communications Systems have been considered as an efficient solution to provide high transmission rates with relative low cost. Optical networks are networks that use optical links connected by optical cross-connectors (OXC) [1]. They can be classified in three types: opaque, translucent and transparent. In opaque optical networks, the signal is regenerated in all intermediate nodes of the lightpath for a given source-destination pair. In transparent optical networks (also known as all-optical networks), the signal is transmitted entirely in the optical domain, without suffering Optical-Electrical-Optical regenerations. In translucent optical networks, some of the nodes have regenerators and the signal can be regenerated in some of them according to a predefined policy. In this paper, we are considering all-optical networks, since they present a lower cost and the constraints imposed by the physical layer are more severe. It occurs due to the noise accumulation and distortion along the transparent lightpath [2] [3].
There are two main challenges in all-optical networks: (i) to design an efficient routing and
wavelength assignment (RWA) algorithm, which has a direct influence in the network performance,
Comparing OSNR based Policies for an
Adaptive-Alternative IA-RWA Algorithm
Applied to All-Optical Networks
Carmelo J. A. Bastos-Filho, Rodrigo C. L. Silva and Daniel A. R. Chaves,
Polytechnic School of Pernambuco, University of Pernambuco, Recife, PE, Bra zil 50.720-001 E-mail: carmelofilho@ieee.org
André V. S. Xavier and Joaquim F. Martins-Filho
and (ii) to obtain an acceptable optical signal-to-noise ratio (OSNR) at the destination node for each
lightpath [2]. These requirements are necessary for providing quality of service (QoS) [4].
The RWA problem consists in to find a route and to assign a wavelength for each connection
request. The RWA process can be classified in two types: static or dynamic [5]. In the static case, the
call requests are known in advance and the RWA operations can be performed in an off-line manner.
The main objective is to minimize the number of wavelengths needed to establish the call requests for
a given physical topology. In the dynamic case, the target is to minimize the blocking probability,
while optimizing the availability of resources. In general, the solution for the dynamic RWA problem
is simplified by decoupling the problem into two separate sub-problems: the routing (R) and the
wavelength assignment (WA) [5]. The performance of a dynamic RWA algorithm can be assessed in
terms of the blocking probability (BP), which assesses the chance of failure in the implementation of a
given network request. It can occur due to the lack of resources or inadequate quality of transmission
(QoT) of the lightpath [4].
Several solutions can be found in the literature for solving the routing problem in optical networks.
In general, they are classified in three types: fixed routing, fixed-alternative routing and adaptive
routing. The fixed routing algorithms always choose the same route for a given source-destination
pair. The fixed-alternative routing algorithm chooses a route from an ordered list of fixed routes
depending on a predefined policy. The adaptive routing algorithms consider the current network state
to determine the routes [5].
Some examples of routing algorithms proposed in previous works are: Shortest Path (SP) [6],
Minimum Hop (MH) and Least Resistance Weight (LRW) [7]. In the SP algorithm, the route is
defined based on the minimum total physical link length. The MH algorithm finds the physical route
with the minor number of optical links. The LRW algorithm finds the routes based on the wavelength
availability aiming to distribute the load over the entire network. One must observe that the LRW
algorithm uses the current information of the network i.e. adaptive algorithm, whereas the two
formers are fixed routing algorithms.
Another relevant aspect of the RWA is the wavelength assignment algorithm (WA). There are some
well known WA algorithms, such as: First-Fit (FF), Random Pick (RP), Least Used (LU), Must Used
(MU) and Distributed Relative Capacity Loss (DRCL) [5]. In this paper, we are considering the MU
algorithm. The MU algorithm selects the most used wavelength in the entire network and it keeps the
spare capacity of less-used wavelengths. We selected the MU algorithm to be deployed in this paper
since it is simple and presents a good performance for WDM networks.
Recently, we have proposed an adaptive-alternative routing algorithm for optical networks, called
NrPSR [8]. The NrPSR algorithm finds the Nr routes that present the lower cost, which are evaluated
based on a cost function expanded in a power series [9]. Then, it chooses one of them based on a
pre-defined policy. In this paper, we propose two alternative policies based on the Optical Signal-to-Noise
lower OSNR that attends the Quality of Transmission requirements. In the second approach, named
NrPSR(OSNRMAX), we select the route that presents the higher OSNR.
The rest of the paper is organized as follows. In section II, we present some related works and a
description of the NrPSR algorithm. In section III, we describe our proposals, the NrPSR(OSNRJE) and
NrPSR(OSNRMAX). In the section IV, we detail the simulation setup and the parameters used in the
simulations. In section V, we analyze the performance of our proposals and compare them to other
policies for the NrPSR algorithm and some other well know routing algorithms. In section VI, we give
our conclusions.
II. RELATED WORK
In this section, we review some contributions that are closely related to this work. Xavier et al. [8]
proposed an adaptive-alternative routing algorithm to solve the RWA joint problem in optical
networks, called NrPSR. The NrPSR pseudocode is shown in Algorithm 1. The NrPSR uses the Yen's
algorithm in order to find the Nr routes with lower cost. Each route is evaluated using the PSR cost
function considering the link length and the link availability as the input variables. The NrPSR can
aggregate the benefits of an adaptive RWA by considering the physical layer effects and can include
information about the wavelength assignment policy since it evaluates dynamically some possible
routes between the source-destination nodes.
Algorithm 1 NrPSR pseudocode.
1: Define the number of routes (Nr);
2: Find Nr routes with minimum cost according to the PSR cost function using the Yen's algorithm;
3: Select the best route among the Nr routes using a predefined policy; 4: return the selected route.
Yen [10] proposed an efficient algorithm to find the Nr paths with lower cost from a source node to
a destination node. This algorithm is more efficient then other approaches because its computational
upper bound increases linearly with the Nr value.
After finding the set of candidate routes to attend to a connection request, the algorithm NrPSR
evaluates each route and selects one of the Nr routes according to a predefined policy. Xavier et al.
[8] proposes the analysis of three policies: Capacity Loss (CL), Minimum Wavelength Matching
Factor (MinK) and Maximum Wavelength Matching Factor (MaxK).
Chaves et al. proposed two approaches to solve the routing problem in transparent optical networks:
Physical Impairment Aware Weight Function (PIAWF) [11] and Power Series Routing (PSR) [9].
Both algorithms use an adaptive link weight function that considers two simple network information
to consider the physical layer impairments. The PSR proposes an expansion in a power series to
evaluate the cost of a link during the calculations of the routes. The first step is to choose the input
The availability xi,j (between the nodes i and j) is defined as [9] [11]: T j i a j i j i x , , ,
, (1)where
ai,j and Tj i,
are, respectively, the number of active wavelengths and the total number of wavelengths in the link from node i to node j.The normalized physical link length yi,j is defined as [9] [11]:
max , ,
d d
yij i j , (2)
in which di,j is the link length between the nodes i and j, and dmax is the maximum link length in the
network.
The second step is to describe the cost function in terms of a power series in agreement with the
chosen parameters [9], as depicted in equation (3).
N n N n n j i n j i n n j i ji y b x y
x f 0 0 , , , , , 0 1 1 0 1 0
,
)
,
(
(3)where f
(
xi,j,
yi,j)
is the cost function associated to the link between the nodes i and j. N is an integerthat represents the number of terms used in the power series expansion.
The third step is to use a global optimizer in order to find the
1 0,n
n
b coefficients for the power series.
The PSR uses the Particle Swarm Optimizer (PSO) [12]. The coefficients are calculated in an offline
manner, i.e. before the network operation. We also chose to use the PSO algorithm because it can
tackle optimization problems in hyper-dimensional search spaces with continuous variables.
The PSO is a population based algorithm and was proposed by Kennedy and Eberhart in 1995 [12].
Each particle l has a position in the search space, that represents a possible solution for the problem.
The positions are updated based on the velocities of the particles. And the velocities of the particles
depend on the best position obtained by the particle during the search process (p
i) and the bestposition obtained by the neighborhood of the particle during the search process (ni
). The equations
used to update the position and the velocity of the particle are shown in equations (5) and (4),
respectively. Algorithm 2 depicts the pseudocode of the PSO algorithm.
1 1 2 2
,
1 i i i i i
i v c p x c n x
v
(4)in which
is the constriction factor [12].
i i
i v x
Algorithm 2 Pseudocode of the PSO algorithm.
1: Generate particles randomly; 2: for all IPSOdo
3: for all IPSO do
4: Evaluate the velocity; 5: Update the position;
6: Evaluate the fitness in the new position; 7: end for
8: end for
9: return the best particle.
Pereira et al. developed a routing algorithm that uses physical layer impairments estimation for the
routing decision, named OSNR-R [4]. The goal of this IA-RWA (Impairment Aware Routing and
Wavelength Assignment) algorithm is to find the route with higher OSNR (Optical Signal Noise
Ratio) for a given wavelength.
III. NRPSR(OSNR) PROPOSALS
In this section, we present two policies for a routing algorithm to solve the RWA joint problem in
all-optical networks. In the first, named NrPSR(OSNRJE), we select the route that presents the lower
OSNR that attends the QoT requirements. This approach tends to reserve resource for further network
requisitions. In the second approach, named NrPSR(OSNRMAX), we select the route that presents the
higher OSNR. This one tends to maximize the QoT of the lightpaths. The NrPSR(OSNRJE)
pseudocode is shown in Algorithm 3 and the NrPSR(OSNRMAX) pseudocode is shown in Algorithm 4.
Both algorithms use the Yen's algorithm to find the Nr routes with lower cost according to the PSR
cost function. After finding the set of routes to attend to a call request, the algorithm NrPSR(OSNRJ E)
evaluates each route and selects the one that presents the lowest OSNR above the QoT criterion and
the algorithm NrPSR(OSNRMAX) evaluates each route and selects the one that presents the highest
OSNR. After the performance evaluation of the candidate routes, if there is no route to attend to the
connection request, the call request is blocked and NrPSR does not test another route.
Algorithm 3 NrPSR(OSNRJE) pseudocode. 1: Define the number of routes (Nr);
2: Find Nr routes with minimum cost according to the PSR cost function;
Algorithm 4 NrPSR(OSNRMAX) pseudocode. 1: Define the number of routes (Nr);
2: Find Nr routes with minimum cost according to the PSR cost function; 3: Select the route of the Nr routes with highest OSNR;
4: return the selected route.
IV. SIMULATION SETUP
We used the SIMTON simulation tool [13] to estimate the blocking probability for the RWA
algorithms. The SIMTON uses the physical layer model described in [4]. For each network
simulation, we run a set of 105 calls randomly generating the source-destination pairs for each
connection request. The connection request process is characterized as a Poisson process and the time
duration for each established lightpath is characterized by an exponential process. After the selection
of a route, if this route is not able to attend to the connection request, either because of lack of
resources or inadequate QoT, the connection request is blocked.
We used two topologies in our simulations. The first is the Pacific Bell, shown in Fig. 1, and the
second is the Finland, shown in Fig. 2. We assume circuit-switched bidirectional connections in two
optical fibers and no wavelength conversion capabilities. The blocking probability is evaluated as the
ratio between the number of blocked connection requests and the total number of connection requests.
The physical layer impairments considered in this paper are: the ASE (Amplified Spontaneous
Emission) and the gain saturation effect in the amplifiers, the PMD (Polarization Mode Dispersion) in
the transmission fiber and the crosstalk in the OXC. The optical parameters used in the simulations
are shown in Table I, where: Psat is the amplifier output saturation power; OSNRin is the OSNR of the
transmitters; Plaser is the output power of the transmitters; OSNRQoS is the minimum OSNR for QoT
criterion; B is the transmission bit rate; Bo is the optical fiber bandwidth; W is the number of
wavelengths per link; Δf is the channel spacing; λi is the lower wavelength of the grid; λ0 is the zero
dispersion wavelength; λ0RD is the zero residual dispersion wavelength; α is the fiber loss coefficient;
LMux is the multiplexer loss; LDemux is demultiplexer loss; LSwitch is the optical switch loss; NF is the
amplifier noise figure; is the switch isolation factor; is the maximum pulse broadening; DPMD is the
PMD coefficient; SDCF is the compensating fiber slope; and STx is the transmission fiber slope.
The coefficients
1 0,n
n
b for the cost function of NrPSR were optimized for a network load of 60
erlang and the simulation parameters used in PSO are shown in the Table II. In order to evaluate the
blocking probability of a given particle, we simulated a set of 105 calls. We used N= 5, where N is the
number of terms used in the PSR cost function. We used the MU as the wavelength assignment
Fig. 1. Pacific Bell topology used in the experiments.
Fig. 2. Finland topology used in the experiments. TABLE I.DEFAULT SIMULATION PARAMETERS
Parameter Pacific Bell Topology Finland Topology
Psat 26 dBm 20 dBm
OSNRin 40 dB 40 dB
Plaser 3 dBm 3 dBm
OSNRQoS 23 dB 20 dB
B 40 Gbps 40 Gbps
Bo 100 GHz 100 GHz
W 20 20
Δf 100 GHz 100 GHz
λi 1528.77 nm 1528.77 nm
λ0 1557 nm 1450 nm
λ0RD 1544.53 nm 1528.77nm
α 0.2 dB/km 0.2 dB/km
LMUX 2 dB 3dB
LDEMUX 2 dB 3dB
LSWITCH 2 dB 3dB
NF 5 dB 6dB
-40 dB -40 dB
10% 10%
DPMD 0.05 ps/km 1/2
0.04 ps/km1/2
SDCF -1.87 ps/km.nm 2
-1.87 ps/km.nm2
STX 0.06 ps/km.nm
2
TABLE II.DEFAULT SIMULATION PARAMETERS USED IN PSO.
Parameter Value Definition
L 30 Numbers of particles
IPSO 200 Numbers of iterations
c1,c2 2.05 Acceleration coefficients 1, 2 U[0,1] Random numbers
χ 0.72984 Constriction factor
S [-1,+1] Search space
V [-1,+1] Velocity limits
V. SIMULATION RESULTS
In this section, we present the simulation results for the network blocking probability as a function
of the traffic load and we perform a load distribution analysis for all investigated RWA algorithms in
order to verify the robustness of the algorithm to deal with load variations along the time.
A. Training Phase
The NrPSR requires a training stage to find the optimized
1 0,n
n
b coefficients. We executed the PSO
to perform the optimization. Fig. 3 and Fig. 4 show the PSO convergence trace for the PSR algorithm
and for four different policies used in the NrPSR: (CL), (MaxK), (OSNRMAX) and (OSNRJE), for
topologies Pacific Bell and Finland, respectively. One can observe that the algorithms converge very
fast and the NrPSR(OSNRJE) algorithm obtained the better performance in terms of blocking
probability.
Fig. 3. PSO convergence trace for Pacific Bell topology using: NrPSR(CL), NrPSR(MaxK), NrPSR(OSNRJE),
Fig. 4. PSO convergence trace for Finland topology using: NrPSR(CL), NrPSR(MaxK), NrPSR(OSNRJE),
NrPSR(OSNRMAX) and PSR.
B. Online simulation - comparison with other algorithms from the literature After the training stage, in which we determined the coefficients
1 0,n
n
b , we compared our two
proposed policies to two other policies for the NrPSR and four other well known routing algorithms:
NrPSR(CL), NrPSR(MaxK), SP, MH, OSNR-R and PSR.
Fig. 5 and Fig. 6 show the blocking probability as a function of the network load for the different
routing algorithms for topologies Pacific Bell and Finland, respectively. NrPSR(OSNR) obtained the
best performance when compared to the other algorithms. For the topology Pacific Bell,
NrPSR(OSNRJE) and NrPSR(OSNRMAX) outperformed all other routing algorithms, mainly for lower
network loads. We obtained better results than the OSNR-R routing algorithm. It occurred because our
approaches balance the load over the network and also reserves resources for future connection
requests. For the topology Finland, NrPSR(OSNRJE) outperformed all other routing algorithms,
including our other proposal, NrPSR(OSNRMAX).
C. Load distribution analysis
In the simulated case shown so far, our proposed algorithm outperformed others routing algorithms.
The results shown in Fig. 5 and Fig. 6 also indicate that our proposals keep its performance level even
for different loads from the one it was optimized in the training stage. It indicates that our proposals
are robust enough to deal with load fluctuations that may occur along the time. Nevertheless, it is also
load distribution fluctuations in the network, which results in a traffic pattern different from the one
considered during the training stage.
Fig. 5. Comparison of the Blocking probability as a function of the network load for the different routing algorithms in Pacific Bell topology.
In this section we investigate the performance of the algorithms as a function of the variations of
the load distribution. Chaves et al. proposed this analysis in [9]. We can state this verification as
follows. Given an uniform traffic matrix T = {ρi,j} (used during the training phase), we produce a
variation in this traffic matrix (i.e. T' = {ρ'i,j}), which might simulate the traffic distribution fluctuation
along the day. T' is obtained from T by the multiplication of each entry by a random number: {ρ'i,j} =
(1 + r) . {ρi,j}, where r is a random number with a uniform distribution in the [-R, R] interval and R is
the maximum allowed load variation per source-destination pair. The T' matrix is normalized to keep
the same total network load. Hence, R=0 corresponds to the case of uniform traffic, whereas R≠0 corresponds to a non-uniform traffic. R = 1.0 represents the case of the traffic load of a given
source-destination pair may increase or decrease by at most 100% of its traffic in the uniform case.
We selected R=1.0 to perform a statistical analysis of the behavior of the RWA algorithms blocking
probabilities. For this purpose, we generated a set of 30 different and independent traffic matrixes. For
each one of these matrixes, we obtained the blocking probabilities from the six considered routing
algorithms. For PSR and the policies of NrPSR, we used the coefficients
1 0,n
n
b values obtained for the
uniform traffic. We present the box plot results in Fig. 7 and Fig. 8. The Box stands for the 50% of the
obtained data, the whiskers correspond to the 100% of the obtained data, the open symbols stand for
the mean value and the horizontal line inside the box represents the median value.
Fig. 7 and Fig. 8 show the Box and Whisker's representations of the statistical analysis of the
performance of the algorithms: LRW, OSNR-R, PSR, NrPSR(MaxK), NrPSR(CL), NrPSR(OSNRMAX)
and NrPSR(OSNRJE), obtained for a set of 30 different, independent and non-uniform (R = 1) traffic
matrixes for the topologies Pacific Bell and Finland, respectively. The NrPSR(OSNRJE) algorithm
outperformed all others routing algorithms in both cases.
Fig. 7. Boxplot chart of the performance of the algorithms: LRW, OSNR-R, PSR, NrPSR(MaxK), NrPSR(CL),
Fig. 8. Boxplot chart of the performance of the algorithms: LRW, OSNR-R, PSR, NrPSR(MaxK), NrPSR(CL),
NrPSR(OSNRJE) and NrPSR(OSNRMAX), obtained for a set of 30 different and independent and non-uniform (R = 1) traffic matrixes in the Finland topology.
We used the Wilcoxon non-parametric statistical test [14] with a significance level of 1%. The
results indicated that the results obtained by the NrPSR(OSNRJE) algorithm are statistically significant
when compared to the results achieved by the other algorithms. Therefore, at least for these two cases,
the NrPSR(OSNRJE) algorithm is the most robust algorithm to deal with load distribution fluctuations.
VI. CONCLUSIONS
In this paper we presented two novel policies to select the lightpath for an adaptive-alternative
impairment-aware routing algorithm for all-optical networks, called NrPSR(OSNRJE) and
NrPSR(OSNRMAX). We performed simulations in the Pacific Bell and Finland topologies using the
Most used WA algorithm. We used a physical impairments evaluation model based on ONSR to
consider the following impairments: ASE noise generation, optical amplifier gain and ASE saturations
and OXC crosstalk.
We compared our proposals to other well known routing algorithms in two different scenarios and
we demonstrated that NrPSR(OSNRJE) outperformed all the others in both scenarios. We also
demonstrated that the performance of our proposal is not mitigated if the network traffic load
distribution changes, which may occur along the time in real world networks.
Both NrPSR(OSNRJE) and NrPSR(OSNRMAX) algorithms require a training stage to determine the
coefficients
1 0,n
n
b before the network operation. This characteristic of a priori knowledge of the
network behavior reduces the computational time for the routing decision process as compared to
noise based online routing calculation approaches.
ACKNOWLEDGMENT
The authors acknowledge the financial support from UPE, UFPE, FACEPE, CNPq and CAPES for
scholarships and grant.
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